THERMAL CONTROL SYSTEM DESIGN FOR AUTOMATED FIBER PLACEMENT PROCESS

Transcription

1 THERMAL CONTROL SYSTEM DESIGN FOR AUTOMATED FIBER PLACEMENT PROCESS Salman Khan A Thesis in The Department of Mechanical and Industrial Engineering Presented in Partial Fulfillment of the Requirements for the Degree of Master of Applied Science at Concordia University Montreal, Quebec, Canada March, 2011 Salman Khan, 2011

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3 ABSTRACT THERMAL CONTROL SYSTEM DESIGN FOR AUTOMATED FIBER PLACEMENT PROCESS Salman khan One of the important concerns about the quality of the thermoplastic composite in Automated Fiber Placement (AFP) process is the degradation of thermoplastic resin, resulting from the overheating or the lack of proper heating by the heating system used in the automated fiber placement machine head. Heat transfer between the heating system and incoming pre-impregnated tow is not easy to control and can result in energy loss or non consistent heating of pre-impregnated tow. The advanced control systems are used to control the key processing parameter of Nip Point Temperature of the Heating System. Two advanced control systems are designed by using the dynamic thermal model of the fiber placement process. One is Linear Quadratic Gaussian (LQG) controller which is implemented to achieve the optimal results for quality performance. The other is Model Predictive Controller (MPC) which is proved more efficient as the physical capacity, safety and performance constraints of the heating system are explicitly addressed in the design of the Model Predictive Controller (MPC). Poly-ether-ether-ketone (PEEK) reinforced with carbon fiber (APC-2) is used as the focused material. The performance of the two control strategies are compared and illustrated through simulations. iii

4 ACKNOWLEDGEMENTS I wish to express my sincere appreciation and gratitude to my professors Dr. W. F. Xie and Dr. S. V. Hoa, for invaluable guidance. I am fortunate to have such excellent and supportive supervisors. The whole thesis would have been impossible without their vision and foresight and trust in me. I am extremely grateful to my friends, for their entire support. iv

5 Dedicated to my beloved parents and dear sisters, Salman v

6 TABLE OF CONTENTS LIST OF FIGURES... viii LIST OF TABLES... xi LIST OF SYMBOLS, ABBREVIATION AND NOMENCLATURE... xii CHAPTER Introduction Motivation Thesis Objectives Thesis Organization Conclusion... 5 CHAPTER Automated Fiber Placement Process And Literature Review Automated Fiber Placement Process Overview Fiber Placement Head Fiber Delivery System Cut / Restart Capability & Trajectory Planning Compaction Heating System Applications Material System Thermal Modeling and Heating Systems Thermal Control System Strategies Conclusion CHAPTER Heat Transfer Analysis In Thermoplastic Composite Fiber Placement Process Thermal Model For Automated Fiber Placement Process Conclusion CHAPTER Quadratic Optimal Control vi

7 4.1 Linear Quadratic Regulator (LQR) Linear Quadratic Estimator (LQE) Linear Quadratic Gaussian (LQG) Control Simulation and Results Disturbance Rejection Conclusion CHAPTER Model Predictive Control Basic Formulation Implementation Optimization and Gain Calculation Simulation / Results of MPC without Constraint Constraints Simulation and Results of Constrained MPC Conclusion CHAPTER Conclusion Contribution of The Thesis Recommendations for future work References vii

8 LIST OF FIGURES Figure 1.1: Automated Fibre Placement Process... 1 Figure 2.1: AFP process overview... 6 Figure 2.2: 6-axis robotic platform made by KUKA robots and fiber placement head... 7 Figure 2.3: PEEK Figure 2.4: Components of thermal model developed by Ku Shih Lu Figure 3.1: Thermoplastic Processing Cycle Figure 3.2: Components of Thermal Model Figure 3.3: Heat conduction with moving heat source Figure 3.4: Three component model Figure 3.5: Three component geometry and boundary conditions Figure 3.6: The first component as volume element Figure 3.7: Process and control Figure 4.1: LQR assuming measureable / available states Figure 4.2: Kalman Filter Figure 4.3: LQG Controller Figure 4.4: LQG Temperature Outputs viii

9 Figure 4.5: Nip- point and pre heater Input powers Figure 4.6: Nip Point Temperature T h Figure 4.7: Temperature T Figure 4.8: Step disturbance Figure 4.9: Nip point temperature T h with step distrubance Figure 4.10: Nip-point heater Input Power with disturbance Figure 5.1: Basic formulation of MPC control Figure 5.2: Flow Chart of MPC process Figure 5.3: Temperature outputs T h,t 1 estimated T 2 with unconstrained MPC Figure 5.4: Nip-point and Preheater input powers Figure 5.5: Constraints in MPC and conventional control Figure 5.6: MPC in Simulink Figure 5.7: Output temperatures with disturbance Figure 5.8: Nip-point temperatures with step disturbance Figure 5.9: Nip-point and Pre-heater Inputs with step disturbance Figure 5.10: Nip-point temperature with constrained MPC Figure 5.11: Nip-Heater temperature ix

10 Figure 5.12: Nip point heater power with constrined MPC x

11 LIST OF TABLES Table 3.1: Specifications and thermal propertires of composite used in simulation Table 4.1:LQG Parameters Table 5.1: Nip-point temperature response in LQG and constrained MPC xi

12 LIST OF SYMBOLS, ABBREVIATION AND NOMENCLATURE Symbol Definition AFP LQR LQE LQG MPC PEEK Automated Fiber Placement Linear Quadratic Regulator Linear Quadratic Estimator Linear Quadratic Gaussian Model Predictive Control Poly-ether-ether-ketone A, B, C System matrices of linear system in state space Q, R Weighing Matrices NN x K L P J u r T m T g T h T 1 T 2 Neural Networks State Variable Regulator Gain Kalman Filter Gain Transformation Matrix between states and co-states Performance Index Control Vector Reference Input Melting Temperature Glass Transition Temperature Nip-point temperature / First Component Second Component Temperature Third Component Temperature xii

13 T a MV N p N c Ambient Temperature Manipulated Variable Optimization Window / Number of Samples Control Horizon F, Φ Pair of matrices in the prediction equation (5.10) K mpc U I Feedback control gain using MPC Parameter vector for control sequence Identity Matrix xiii

14 CHAPTER 1 INTRODUCTION 1.1 MOTIVATION Automated Fiber Placement (AFP) is a process in which strips of unidirectional composite prepreg tape, normally called tow (which is a combination of unidirectional individual fibers, pre-impregnated with thermoset or thermoplastic resin) is collected and laid-up on the mandrel or mold with the help of automated mechanical system. In AFP process the automation starts from the delivery, followed by preheating of the composite material for smooth lay-up on the mold surface under controlled Nip-point heat and pressure as shown in Figure 1.1. Figure 1.1: Automated Fiber Placement Process The above process exists for both thermoset and thermoplastic composite material, however thermoplastic offers one step completion of the process, in which bonding is 1

15 done simultaneously without any requirement of post processing. This process is widely known as in-situ consolidation of thermoplastic composite. Compared with thermoset, thermoplastics are more suitable for automated placement process as the combination of thermoplastics with robotics offers tremendous potential in high performance composite structures manufacturing. AFP is considered superior to conventional methods of manufacturing composite structures, especially in terms of quality and cost. AFP is now extensively used in aerospace industry, making parts like fuselage components, empennage structure, fighter aircraft intake ducts, engine nacelle components, space launch vehicles components etc [1]. The process can be divided into four important sub-systems: 1) Delivery of composite material and trajectory planning for placement; 2) Heating of the composite material; 3) Pressure application; 4) Compaction of the material on the mold surface. Out of the above sub-systems the most important feature of AFP machine, especially when dealing with thermoplastics is the heating system. Energy from the heater melts the surface of the material, while at the same time pressure is applied to compact the material on the mold surface. The choice of the heating system is unique and largely depends on its application. For better quality in both high speed and high temperature production, a powerful and controlled heating source has to be incorporated into the fiber placement machine head. 2

16 AFP process strongly depends on the precise control of the heating parameter and for the optimal results, the parameter is chosen according to the process heat transfer model and in some cases from the material test data. One of the reasons for increased popularity of AFP process is cost effectiveness [2], and the selection of heating parameter during manufacturing of composite structure has a significant effect on cost and quality of the finished product. 1.2 THESIS OBJECTIVES The selection of processing parameters has significant effect on the quality of the final product. One of the important processing parameters in automated fiber placement process is heat intensity. It should be carefully selected and controlled during the process which can be achieved by improving control system design. Thermal model based control of the heat intensity is the objective of this study. AFP process faces some significant hurdles which need to be overcome. The main problem identified is the economic losses due to degradation of material during the process. Therefore advances continue to make the process affordable and flexible. Most of the research in the field of AFP process is focused on the process modeling and very few researchers have suggested control strategies for the heating system of AFP machine. The objective of this study is to provide the essential knowledge about AFP process, to identify the importance of critical heating parameter of the process, and to propose thermal control strategies which help in developing an economical automated work cell for AFP process. 3

17 Automated process of fiber placement is used for composite manufacturing of aerospace structures, thus the technology is mostly used by large companies [1]. However the process has greater potential to be a part of common industrial setup as composite material is becoming a main stream material for industrial applications. This study will support the efforts of manufacturing a low cost prototype system for different commercial applications. 1.3 THESIS ORGANIZATION Chapter 2 gives the introduction of the basic components of AFP system. A brief description of the heating systems employed in AFP process is presented with a literature review on the application, thermal modeling and the control strategies previously used to control the heating system. Chapter 3 explains the AFP process model used as a plant for proposed control strategies and gives an insight on thermoplastic composite material. Chapter 4 proposes Linear Quadratic Gaussian (LQG) control strategy for the thermal control in AFP process. LQG is a fundamental optimal control problem, which focuses on the linear system with disturbances. Optimal control finds the control law for a system such that a specific optimality criterion is achieved. LQG controller is simply a combination of Kalman filter i.e. Linear Quadratic Estimator (LQE) with a Linear Quadratic Regulator (LQR). LQG controller shows improved performance, however limitations are observed when AFP plant is subjected to step disturbance. 4

18 Chapter 5 presents a control strategy based on Model Predictive Control (MPC). MPC is an advanced method of process control based on the iterative finite horizon optimization of the plant model. It predicts the behavior of the temperature at the Nip-point of the heating system with respect to the input. MPC not only handles the disturbance but also addresses the limitations of the heating system and the material safety requirements, when subjected to step disturbance through MPC constraint application. Chapter 6 gives the conclusion of the thesis and recommendations for future work. The references follow Chapter CONCLUSION In this chapter, AFP process is described with emphasis on the importance of thermal control. The research objectives of this thesis project are discussed and the thesis organization is outlined. Before explaining the heat transfer model and the thermal control system techniques, one should understand the basic working of Automated Fiber Placement and the concerned literature available. 5

19 CHAPTER 2 AUTOMATED FIBER PLACEMENT PROCESS AND LITERATURE REVIEW 2.1 AUTOMATED FIBER PLACEMENT PROCESS OVERVIEW AFP process offers high production rate, better quality, efficiency and low cost manufacturing of large scale composite structures. Automation has become an important part of composite manufacturing as it provides a way to reduce the manufacturing cost, in terms of labor hour, reduction in material scrap, good processing quality and repeatability of process through use of efficient control and automation technology. AFP process is the combination of a number of processes as shown in Figure 2.1 [3]. Integration of Robotic Platform and AFP head Fiber path generation and Trajectory planning AFP PROCESS Process Parameters Feedback Control of Process Parameters Figure 2.1: AFP process overview 6

20 Fiber placement head is mounted on robotically controlled multi-axis platform. Prototypes of different fiber placement heads have been designed and manufactured, and most of them are mounted on 6-axis gantry robotic system as shown in Figure 2.2 [4]. Figure 2.2: 6-axis robotic platform made by KUKA robots and the fiber placement head [4] 2.2 FIBER PLACEMENT HEAD All the main functions of AFP process are executed through fiber placement head. It provides the feed, heating, consolidation, cutting, placement, and lamination of the material on the mold or tool surface. The fiber placement head is manufactured according to the application and raw material [5]. The key features of AFP head are: 1) Fiber Delivery System 2) Cut/Restart Capability 3) Compaction 4) Heating System 7

21 2.2.1 FIBER DELIVERY SYSTEM The delivery of fiber to the head is very important for the process flow and it should not restrict the operating zone of the AFP. In larger machines, material is delivered in the form of collimated band of tows, through the rollers located at the creel and the head. The lay out speed of individual tows is controlled by independent delivery guide system from the spool to the compaction system of the head. The system also controls the band width, during lamination in curved path CUT / RESTART CAPABILITY & TRAJECTORY PLANNING AFP heads have the capacity of automatic cutting and restarting of the tows, making it possible to cut, clamp and restart without stopping the laminating procedure of the head. Cut/Restart sequence is programmed using off-line software, based upon the lay-up geometry during the path generation and simulation in CAD. Traditionally the teach pendant to jog the robot to the desired place is used, but these days trajectory planning is carried out offline [6]. Trajectory planning just provides the starting point, however the most important parameters like compaction force and heating temperature should be monitored and controlled separately COMPACTION Compaction is the pressing system installed in the fiber placement head. The function is to press the tow onto the part or mold, so that entrapped air and inner band gaps are removed. In most situations, it is necessary to introduce heat into the compactor to decrease the resin viscosity of the tows. The process is referred to as tack enhancement. Increased tack enables the incoming fibers to adhere more quickly and remain in place on the mold or substrate. Uniform compaction produces a higher quality parts, eliminates 8

22 debulking, processes concave surfaces and provides greater flexibility in fiber steering. Different types of hydraulic and pneumatic compaction system have been used in AFP head for application of compaction force. For the better quality results the consolidation process has been investigated by many researchers, and still under investigation. To investigate the effect of the compaction force variations in the consolidation process, knowledge of compaction model is required, which is beyond the scope of this study HEATING SYSTEM In selection of the heating system, the important factors are the size, flexibility and price. Several types of heating system are used in the AFP head [7], and the most common systems include: laser heater, hot roller/shoe heater and hot gas heating Laser Heater High frequency waves can heat the material by causing the molecule in the thermoplastics to oscillate. This method is used in thermoplastics containing polar molecules. The laser heat generation is a difficult and expensive process. Lasers offer high efficiency and the better response time, which makes the system suitable for nippoint heating in moving fiber placement head; however the industry is reluctant to adopt the technique due to higher equipment cost and safety requirements Hot Rollers / Shoe Heater Heating through the rigid system of roller or shoe is less expensive and regarded as a safest option. Open flame and acetylene gas torch provides a high density of energy. Usually they are so hot that they may degrade the polymer. Efficiency of rigid heating system is more than the hot gas and less than laser, researchers have closely monitored 9

23 the performance of heating system for AFP of thermoplastic and simulation results have shown that rigid heating system is the most promising and outstanding system [5]. Most attractive attributes of rigid heating system are the cost and size which add to the flexibility requirements of AFP head, making the system the better option. The requirements of the systems are the precise control of heating filament and to prevent the heated composite to stick with the heat source Hot Gas Heating Nitrogen gas is normally stored in high pressure vessel and the liquid form is heated electrically by a torch and then blasted through a nozzle, specially designed to provide a uniform convective heat source. The two important reasons for the common use of hot gas heating system for AFP process involving thermoplastics are, the minimum equipment cost and the traditional use of hot gas heating system for welding of thermoplastic. Hot gas heating system is capable of heating the nitrogen up to 1200 C. Optimum processing conditions for on-line consolidation of thermoplastic using hot gas has been investigated in details [7], and now the hot gas system is used extensively. 2.3 APPLICATIONS Automated fiber placement process is widely used in aerospace industry. Since 1980s the technology has developed into a highly dependable process. It offers lower material scrap, reduced lay-up time, improved safety and quality standards, process repeatability and complex parts manufacturing. The scrap rate in automated process is about 3%-8%, which is much less than 20%-50% scrap rate in manual processes [2]. The reduced scarp rate is a major contribution to the cost reduction offered by automated process. Automated placement process is now part of larger operations of well known companies, 10

24 and is extensively employed in aircraft manufacturing. It accounts for 25% of the airframe of aircraft like C-17 AirLifter, F-18 Super Hornet, F22 Raptor Joint Strike Fighter [2]. Commercially available automated tape laying machines offered by Cincinnati Milacron and Ingersoll are widely used for the manufacturing of wing skins and control surfaces of B2 aircraft from Boeing and stabilizer skins for Airbus Industries [8]. As the applications of the AFP are becoming numerous, special attention has been given to the manufacturing of complex aerospace structures. Automated Dynamics Corporation has succeeded in manufacturing of complex structures like, Helicopter Drive Shafts for Bell Helicopters, Monocoque Tail boom, V22 main rotor grip element of helicopter [9]. Automated Fiber Placement facility developed by NASA Marsch Space Flight Center uses the facility for manufacturing complex 3-D aerospace structures. NASA Langley Research Center has proved a valuable asset for obtaining data, experience and insight in automated fabrication of high performance composites [10]. Robotic Platform (6-axis robots) provided by KUKA robotics and ABB are normally used for the automated fiber placement machines [3]. User interface software like Labview are used as the interacting control software, CADFiber and CATIA CPD V5 R18 softwares are used for laminate design, simulation and programming [11]. Robotic Fiber Placement facility at Robotics and Mechatronics Research Laboratory in Monash University is widely used for the research on the trajectory planning and control of automated fiber placement process [12]. Companies like Composite Systems provide the composite tooling for the automated machines, and develop the placement head designs 11

25 [13]. Cytec Engineering Material Company is using 12 tow in situ consolidation head for automated tape laying machine for commercial industrial applications [14]. 2.4 MATERIAL SYSTEM Compared to thermosets, advanced thermoplastics are relatively new, and are now extensively used in commercial applications. Although the market is dominated by composites process with thermoset matrix resin, a range of commercial composites based on advanced thermoplastic matrix resins have emerged for high temperature applications. Thermoplastics in general have no shelf life, low moisture absorption, thermal stability, high toughness/damage tolerance, short processing cycles, potential for manufacturing cost reduction, ability to be remolded and reprocessed and repaired by applying heat and pressure [15]. However the limited commercialization of thermoplastic products is due to its high cost. Thermoplastic polymers are usually linear molecules with no chemical linkage between the molecules. The molecules are held together by weak secondary forces, such as van der waals or hydrogen bonding and are readily deformed by the application of heat and pressure. During the consolidation process the changes are substantially physical [16]. The term Advanced Composite normally implies to the high volume fraction reinforcing agent of order 60wt%. Resins for advanced composites can be classified according to their chemistry. Thermoplastics based on aromatic polymers like Poly-ether ether-ketone (PEEK), have better mechanical properties, high temperature capability, and are considered equivalent or even better than the thermosets. In its chemical structure the dominant characteristic is the polymer backbone as shown in the Figure

26 Figure 2.3: Poly-ether-ether-ketone (PEEK) In this study, Poly-ether-ether-ketone (PEEK) matrix, reinforced with 60% graphite fiber is used as a material system for simulation study. PEEK was introduced by Imperial Chemical Industries (ICI) in 1981 with the trade name of Victrex PEEK [17]. PEEK has been the focused material for many researchers working on the automation of thermoplastic manufacturing process [18-28]. PEEK resins have melting and processing temperatures that are well suited to the technology available at the present time. Thermal stability of PEEK is very reliable within the processing temperatures, making it an ideal material for high temperature applications and replacement for metallic aircraft components. PEEK AS-4/APC-2 composite is of a high quality pure grade that contains no special additives. The results of numerous tests conducted on PEEK AS4/APC-2, indicate that this material demonstrates satisfactory behavior to aerospace environments and is insensitive to moisture [29]. In automated process the potential problem with auto consolidation is lack of consolidation due to insufficient diffusion time. Effect of heating rate and short melt times on the required processing conditions of PEEK thermoplastics are discussed in detail by Muzumdar [30]. The detail understanding of the material and the heat transfer model of the process is very important for the efficient thermal control. 13

27 2.5 THERMAL MODELING AND HEATING SYSTEMS A few important thermal models describing the temperature distribution in automated process are discussed. In these models different heating sources have been employed like nitrogen torches, laser scanning and rigid contact. Ku Shih Lu [31] employed nitrogen gas heating system and develop a simplified model to simulate the temperature distribution. The proposed model consists of the roller, tail compactor, heating source (nozzle), and composite and the study discusses the roller contribution in heat distribution. Figure 2.4: Components of thermal model developed by Ku Shih Lu [31] Nitrogen source is a convective heat source. Eulerian frame of references is adopted to arrive at steady state temperature distribution. Roller and tail compactor need detailed knowledge of consolidation mechanics which is beyond the scope of the current study and the focus of this thesis remains on the temperature control. Muzumdar [30] developed a similar model by considering the laser assisted heating, to determine the 14

28 temperature, heating rate, cooling rate, melt time and consolidation force as a function of time and position for a given heat intensity, tape speed and consolidation force. The information on temperature history is very important to predict and control the processing parameter, which needs a suitable heat transfer model. A process model which relates the heat intensity, tape speed and consolidation force to the temperature history is presented for online tape consolidation process. Po jen Shih [32] employed the Nitrogen and Laser Heating sources to create the molten zone and adequate pressure is applied to achieve the consolidation for PEEK APC-2 material automated system. A focused heat source was aimed at the interface between incoming towpreg and substrate to create a molten zone. The intensity of the heat source must be properly adjusted to ensure the melting on both mating surfaces. In this study it was identified that when the feed speed was too high, the single point heating was not enough, therefore, preheating stage was required to elevate the temperature of the incoming tape. Andersen and Colton [33] discussed the importance of pre-heating stage. Pre-heating is required for two reasons, i.e. The heat capacity (C c ) of the thermoplastic composite is too high and the transverse thermal conductivity (K z ) is fairly low, which makes it very difficult to quickly heat the pre-preg tape from room temperature to the processing temperature. In addition the accurate control of pre-preg temperature is highly desirable. Therefore the material is maintained at the elevated temperature, close to but less than the processing temperature, and finally pre-preg passes into the final heating stage where it is brought to the processing temperature. Wordermann and Friedrich [34] used the 15

29 experimental setup to study the consolidation process and recorded the temperature profile to verify the heat transfer model. 2.6 THERMAL CONTROL SYSTEM STRATEGIES Some control system methodologies used by the researchers to control the heating system mounted on the automated fiber placement head are discussed and an insight is given on the importance of the temperature control in automated process. Temperature and pressure at the nip point are key process variables to be controlled to ensure successful in-situ consolidation. Dirk Heider and J Gellespie [35] used the PID and NN (Neural Networks) based control on CMAC (Cerebellar Model Arithmetic Computer) to develop an adaptive temperature control system for thermoplastic based automated fiber placement. The composite material used in this study was PEEK (APC-2), the nitrogen gas heating system was employed with AGEMA thermal camera as a feedback sensor. The objective was to maintain the temperature under the nip point according to the set point to achieve highquality. The CMAC was trained both online and offline to lower the heat transfer behavior of the system and the desired heat profile, at the nip point the heating was compared with the model output to find the suitable process input. The conventional PID was observed to be very noisy especially in the presence of disturbance, mainly because of slower response to the observed changes in the profile. Increasing the response times leads to unstable control system which reacts more on the noise. At the set point temperature of 440 C, an approximate deviation of 15 C was observed. 16

30 PF Lichterwainer [36] developed a NN based Controller to control the heating system for the automated fiber placement machine. The objective was to improve the temperature tracking performance. Inverse model of the AFP process was used for the online training of the neuro-controller to improve the performance. In this study the laser heating system was used, which provided better response time as compared to nitrogen gas system. A focused IR camera was used as a feedback sensor. Wei-Ching Sun and W Lee [24] developed a process thermal model for automated planned of thermoplastic and developed a LQR based control methodology to control the thermal heating system for achieving high quality thermoplastic composites laminate. PEEK (APC-2) material system was used in the study and a low cost moving rigid contact nip point heater with nitrogen gas pre-heating was used as the process components. The goal was to control the bond quality of thermoplastic laminates during the manufacturing by effective control of heating system. M Lee [37] used PID controller to control the heating system for automated fiber placement process, the study was focused on the selection of heating system and it was proved that Rigid Contact heating system with PID controller was more efficient than nitrogen gas and was more economical compared to the laser systems. Artificial Neural Network (ANN) was also used in open loop optimization for the automated thermoplastic composite tow placement system [38]. Neural network (NN) based process model was developed to predict material quality as a function of process set points. The set points are based on experiments and experience. ANN based model facilitate the in-situ optimization of the important process parameters, however the focus 17

31 of the study was the bond quality and heating and the laminates contact model were used to predict the ideal conditions. 2.7 CONCLUSION In this section an overview of AFP process is presented and the components of AFP machines head are discussed. An insight is given on available heating systems mounted on the AFP head. The literature review is presented on the automated placement process, the material system, the thermal model of the process and some control system methodologies used by researchers to control the heating system, especially for thermoplastic material. Before designing the control strategies, the thermal model of the process needs to be understood in detail; therefore the next chapter is devoted to the thermal model of the AFP process. 18

32 CHAPTER 3 HEAT TRANSFER ANALYSIS IN THERMOPLASTIC COMPOSITE FIBER PLACEMENT PROCESS In any thermoplastic polymer the thermodynamics associated with temperature change plays an important role in predicting the process parameters. Thermo physical effects at higher processing temperatures are very significant. Not only the temperature level reached but also the time spent on reaching that temperature is important [39]. The time required to reach the consolidation temperature is a function of the heating method and consolidation temperature values of specific thermoplastics. However for semi-crystalline material like PEEK AS4/APC-2, it should be above melting temperature (T m ). The consolidation time is usually long for the amorphous thermoplastics, since they do not melt and generally maintain higher viscosities at the processing temperature [40]. As a rule of thumb the glass transition temperature (T g ) is approximately 2/3Tm (temperature in K). The consolidation of melt fusible thermoplastic consists of heating, consolidation and cooling as shown in Figure 3.1 [41]. Figure 3.1: Thermoplastic Processing Cycle [41] 19

33 Appropriate selection and arrangement of the heating sources are the most important factors for the successful on-line consolidation of system. However it is very difficult to physically measure the change in temperature in the deformation zone, therefore a model consisting of all the mechanisms involved in consolidation is required for the vital temperature information. To develop a thermal model, the physics involved in consolidation must be carefully analyzed. The entire structure of the process is very complicated therefore the focus of this study is on the thermal analysis and control. 3.1 THERMAL MODEL FOR AUTOMATED FIBER PLACEMENT PROCESS The thermal model captures all the major thermal effects so that an accurate prediction of temperature distribution of the composite can be made. Although the entire structure of the in-situ consolidation process is complicated, a simplified thermal model of in-situ thermoplastic composite tape laying process is considered [24]. Figure 3.2 gives all the major components of the thermal model. Incoming Composite Material Pre-heater Foot Heater Shim Shim Velocit Existing Laminate Nip-point heating Nip-point heating Tool Figure 3.2: Components of thermal model 20

34 In Figure 3.2 the incoming composite material is assumed as thermoplastic composite PEEK (APC-2) with 60% of graphite fiber, the nominal processing temp of PEEK is approximately 387 C and its manufacturing process window is assumed to be from 375 C to 400 C. For the nip point heating a rigid heating source of foot heater is used, as the rigid heating sources are the most economical as compared to other heating sources [5]. The source is assumed to be an equipment of power 80Watts, however the only requirement of this type of system is to prevent the heated composite to stick with the heat source, therefore a shim is used to address the problem as shown in Figure 3.2. A ceramic tool plate is selected for the model and the heater velocity (V x ) as shown in Figure 3.3 is fixed at 25mm/s, with appropriate temperature control a good quality laminate is achieved at this velocity [42]. Using the arrangement, the temperature at the critical locations in the process is predicted. Considering the critical inter-laminar bonding, the temperature at the Nip-point and at the interface between the top ply and the ply previously laid (substrate) is very important for achieving the quality product. The process is considered as a two dimensional heat conduction process with moving heat source as shown in the Figure 3.3. Composite Lamination Heater z V x z x y Figure 3.3: Heat conduction with moving heat source 21

35 To achieve the process model, the process dynamics shown in Figure 3.2 and 3.3 are divided into three components, based on the temperature of the critical locations in the process as shown in Figure 3.4 and 3.5. Figure 3.4: Three component model Figure 3.5: Three-component geometry and boundary conditions 22

36 T h T n T 1 T 2 Figure 3.6: The first component as volume element Consider the first component T h in Figure 3.5 as the volume element shown in Figure 3.6 for the determination of the heat conduction equation. The rate of heat transfer in z direction is given by general heat transfer equation (3.1) [51]. (3.1) in z direction equation (3.1) is written as: (3.2) where Q= Total heat flow in the block. K z = Thermal conductivity in z direction 23

37 There are many analytical solutions of the equation (3.1) for a wide variety of initial and boundary conditions; here equation (3.2) is solved using the finite difference method using the boundary conditions shown in Figure 3.5 [52]. The finite difference method begins with the discretization of the space and time such that there is an integer number of points (n) in space and time at which we calculate the field variables, in this case just the temperature. For simplicity consider the volume element in Figure (3.6), using the boundary conditions shown in Figure 3.5 and the finite difference the energy balance for equation (3.2) is presented as in equation below. Here Q h represents the input heat from the nip point heater. The first component shown in Figure 3.5 contains the Nip-point foot heater and the concerned temperature is the Nippoint temperature T h. This is the actual lay-up stage and the precise control of T h is the primary objective. Therefore the total heat in Nip-point heater component is given by equation (3.3). (3.3) 24

38 where K hz = K sz = Thermal conductivity of heater/shim component in z direction t= Time step =0.001seconds The concerned temperature in the second component shown in Figure 3.5 is T 1. It represents the highest bonding temperature between the layers and is an important indication of the bond quality. Using the equation (3.2) for the second component in Figure 3.5, considering tool temperature is equal to ambient, and balancing the energy, the linear heat equation (3.3) is achieved. (3.4) where K cx = Thermal conductivity of composite in x direction K hcx = Resultant of thermal conductivities in x direction K ctz = Resultant of thermal conductivities in z direction In the third component shown in Figure 3.5, T 2 represents the temperature when the foot pressure is removed. T 2 is used to estimate the spatial variation of the bond temperature and it affects the rate of crystallization [39]. By balancing the energy in the second component the equation (3.5) is achieved. 25

39 (3.5) The values of all parameters and material properties are defined in Table 3.1. Table 3.1: Specifications and Thermal Properties of Composite used in Simulations [43] D= Component length= 0.05(m) K cx = Composite conductivity in X direction : 6.0 (W/m C) H t = Tool plate thickness: (m) K cz = Composite conductivity in Z direction: 0.72 (W/m C) H h = Heater height: (m) (K sx =K sz )= Shim heat conductivity: 20.9 (W/m C) H c = Composite thickness : (m)*ply# h n = Heat transfer coefficient hn: 60 (w/km 2 ) h s = Heater transfer coefficient hs: 960 (W/km 2 ) (K tx =K tz )= Ceramic heat conductivity: 1.96 (W/m C) C c = Composite Specific heat : 1425 (J/Kg C) C h =C s = Shim/Heater specific heat: (J/Kg C) W= Component width: (m) C t = Ceramic specific heat: 1.21 (J/Kg C) ρ c = Composite density : 1560 (kg/m 3 ) ρ h =ρ s = Shim/Heater density: 7750 (kg/m 3 ) T a = Ambient temperature=tool Temperature=0 C K hcz = K hcx = 0.695(W/m C) Ceramic density (ρ t )= 1331 (kg/m 3 ) K ctz = 0.526(W/m C) 26

40 Applying the values of parameters given in Table 3.1 and rearranging equations (3.3), (3.4) and (3.5). (3.6) (3.7) (3.8) Express the equations (3.6), (3.7) and (3.8) as a linear matrix equations in the form of x where x(n) is a state vector, u(n) is the input and. and 27

41 B = The matrices B are functions of material properties, boundary conditions, element size, and velocity. Setting ambient temperature to zero, a discrete time state space model with two inputs and three outputs is developed as shown in equation (3.9). (3.9) For the above linear system, the control objective is to control the three temperatures T h, T 1 and T 2 as represented by vector x(n), to the pre-defined desired values by using the heater power and pre-heater inputs represented by vector u(n), y(n) represents the system output and C is the identity matrix assuming all the state variables are measurable. Two kinds of optimal control strategies are developed to fulfill the tasks in Chapters 4 and 5. The idea is to control the temperature effectively during the process by using the thermal prediction of the model, but the variations in thermal properties and disturbances are not predicted and therefore a closed-loop control system is required as shown in Figure 3.7, for the online temperature regulation to keep the bonding temperature within the manufacturing process window and to reject the undesired disturbances. The temperature at the important locations are monitored and controlled throughout the process, and the simulation results show the effectiveness of the control methods. 28

42 AFP process Thermal properties +Process variable + Disturbances Controller and Estimator Sensor Figure 3.7: Process and Control 3.2 CONCLUSION The chapter provides some knowledge about the material used in the AFP manufacturing and the thermal model of AFP process. PEEK thermoplastic material is used and the heat transfer during the process is explained. Thermal history of the process has a significant effect on the mechanical properties and the final part quality. The process model is developed using the basic heat conduction equation as the heat transfer plays an important role in the lay-up and consolidation of thermoplastic material. This thermal model of automated placement process is used for the control of the critical temperature parameter. 29

43 CHAPTER 4 QUADRATIC OPTIMAL CONTROL One of the mathematical optimization methods used to design the control system is the optimal control. Optimal control problems are very common in control area. The main idea in optimal control system is to find a control law for a given system by optimizing a specific function which is called the cost function. The cost function is the function of state and control variables, and this function is chosen as the performance index. Optimal control is achieved by solving Hamilton-Jacobi-Bellman equation. The value chosen for performance index indicates how well the measured value of the system matches the reference signal. Therefore the performance of the system is optimized by selecting the control vector in such a way that performance index is minimized. The selection of performance index or the cost function is very important and is a difficult process for complex systems because it determines the nature of control and is derived according to the requirement of the process. It is possible that a control system optimized under one index is not optimal in terms of others [44]. Optimal system design is to minimize the performance index which determines the configuration of the system. Analytical solution of optimal problem provides the complete information about optimal structures. The optimal control design for a linear system is usually based on quadratic performance index, which has been widely used in practical control system design as a measure of system performance. Quadratic performance index has been used in our optimal control system design for Automated Fiber Placement thermal process, which is modeled as a linear system. Let us consider the AFP system model described earlier in 30

44 equation (3.10). In the quadratic optimal control problem we desire to determine a law for the control vector u(n), as shown in equation (4.1), such that a the quadratic performance index (4.2) [47] is minimized. u (4.1) (4.2) Q and R are positive definite Hermitian matrices. In equation (4.2) the first part in summation brackets accounts for the relative importance of error during the control process and the second term accounts for the expenditure of the energy of the control signal [44]. If N= the optimal control gives a steady state solution and the gain matrix K(n) in equation (4.1) becomes a constant matrix. The focus remains on determination of matrix K(n) and the performance index written as in equations (4.1) and (4.2). 31

45 4.1 LINEAR QUADRATIC REGULATOR (LQR) A specific type of linear quadratic optimal control problem is that of a linear Quadratic Regulator (LQR), in which all the matrices (i.e. A, B, Q and R) are constant. The LQR tries to regulate the [ ] for the reference signal tracking, and the classical optimal control theory represent the LQR in feedback form as shown in the Figure 4.1. Pre-computation of K(n) AFP Process r (n) + - K(n) u(n) Y Figure 4.1: LQR assuming measureable / available states. The weighting matrices Q and R, weighs the relative importance of the performance caused by the state vector x and control vector. Different approaches have been used by researchers to select Q and R, where selection is made either by trial and error or by using practical, iterative procedures [46]. The next step is to find the regulator gain K in control law equation (4.1), where the steady state gain K is represented as in equation (4.3) [47]. (4.3) where P represents the transformation matrix between states. The solution of P is achieved by solving steady-state Riccati equation [47] given by equation (4.4). (4.4) 32

46 In the above optimal control design shown in Figure 4.1, it is assumed that all the states are available and the outputs are measurable. Considering the actual situation, the Nip point temperature T h and the first component temperature T 1 as shown in Figure 3.4, can be readily measured by using high temperature pyrometer which is normally used in advanced Automated Fiber Placement machines, and provides a non-contacting procedure of measuring thermal radiations. However the third component temperature T 2 is hard to measure during AFP manufacturing process, therefore a Linear Quadratic Estimator (LQE) or Kalman estimator is designed to estimate this temperature. 4.2 LINEAR QUADRATIC ESTIMATOR (LQE) In control theory Kalman filter is most commonly represented as linear quadratic estimator (LQE). Kalman Filter provides the estimates of the measurements by prediction. It estimates the uncertainties in the prediction and finally computes the weighted average of the prediction and measured values. The weighing matrix helps having the estimates close to the true values. Kalman filter is designed based on the system model. It provides the estimations of the immeasurable state variables by using the inputs to the system and partial measurable state variables (output measurements). The design of Kalman filter takes into account the noise and uncertainties. It also averages the predictions with new measurements using weighing matrices. This process is iterated in every sampling interval. 33

47 u w (noise) AFP PROCESS (PLANT) u y KALMAN FILTER (PLANT) v (noise) Figure 4.2: Kalman Filter Consider a discrete time system subject to Gaussian noises w and v, in equation (4.5). (4.5) The noise covariance represented in equation (4.6): (4.6) The estimator is given in equation (4.7) [47], where represents the estimated states. (4.7) The Kalman filter gain L in above equation is obtained by solving Riccati equation (4.8). (4.8) 34

48 The error covariance matrix P is given by: (4.9) 4.3 LINEAR QUADRATIC GAUSSIAN (LQG) CONTROL Linear Quadratic Gaussian (LQG) controller is the combination of Linear Quadratic Estimator (LQE) and Linear Quadratic Regulator (LQR). It concerns uncertain linear system disturbed by additive white Gaussian noise, in condition where the state variables are not available for feedback control. Figure 4.3 shows the application of white noise as process and sensor disturbance and implementation of LQG Control. Process Noise Disturbances Reference Temperatures + - LQR Controller u AFP Process Contro Output Temperatures (T h, T1) Kalman Estimator Figure 4.3: LQG Controller 35

49 4.4 SIMULATION AND RESULTS We use Matlab/Simulink to carry out the simulation of LQG optimal controller as shown in Figure 4.3. The simulations are done using fixed time-step size of 1ms and the discrete time solver, with simulation time of 30 seconds. Using the optimal control theory and equations (4.3), (4.4), (4.8) and (4.9), the regulator gain K, the weighing matrices Q and R, the Kalman filter estimator gain L, and the error covariance matrix P are calculated as shown in Table 4.1. Table 4.1: LQG parameters Regulator Gain K Weighing matrix Q Weighing matrix R Kalman filter Gain L Error covariance matrix P 36

50 Heater Power (Watts) Temperature (centigrade) According to the conditions defined in Chapter 3 for thermoplastic composite PEEK (APC-2),where the manufacturing process window is from 375 C to 400 C [43] and the parameters defined in Table 3.1, the simulation is carried out for the system in Figure 4.3.The reference temperature for Nip-point heating T h is set as 400 C. Figure 4.4 shows the output temperatures T h, T 1 and the estimated temperature T T h T T Time (seconds) Figure 4.4: LQG Temperature Outputs T h, T 1 and the estimated temperature T Q h Pre-Heater Time (seconds) Figure 4.5: Nip- point and Pre heater Input Powers 37

51 Temperature T1 (Centigrade) Temperature Th (Centigrade) Figure 4.6 and 4.7 shows the response curves of the Nip-point temperature T h and the first component T T h X: 0.03 Y: Time (seconds) Figure 4.6: Nip Point Temperature T h (Steady State Error = 0.62%, Rise Time = 0.03 sec, Settling Time = 0.1 sec) T Time (seconds) Figure 4.7: Second Component Temperature T 1 (Steady State Error = 0.44%, Rise Time = 0.03 sec, Settling Time = 0.08 sec) 38